Three-dimensional metamaterial device with photovoltaic bristles

ABSTRACT

The systems, methods, and devices of the various embodiments provide a photovoltaic cell made up of an array of photovoltaic bristles. The photovoltaic bristles may be configured individually and in an array to have a high probability of photon absorption. The high probability of photon absorption may result in high light energy conversion efficiency.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.13/751,914 entitled “Three-Dimensional Metamaterial Device withPhotovoltaic Bristles” filed Jan. 28, 2013, the entire contents of whichare hereby incorporated by reference.

FIELD

This application generally relates to photovoltaic devices, and morespecifically to photovoltaic cells featuring a large number ofphotovoltaic bristles.

BACKGROUND

Solar energy is a popular clean energy, but it is generally moreexpensive than its carbon based competitors (e.g., oil, coal, andnatural gas) and other traditional non-carbon based energy sources(e.g., hydropower). Typically, solar energy is also relatively expensivebecause traditional photovoltaic cells with a planar configuration havegenerally low total efficiency. Total efficiency is based upon the totalpower produced from a solar cell throughout the day as the sun transitsacross the sky. Total efficiency is different from the theoreticalefficiency of converting to electricity a given amount of light energystriking the photovoltaic cells with a zero angle of incidence (e.g.,the instant when the sun is directly above the solar cell).

SUMMARY

The systems, methods, and devices of the various embodiments provide aphotovoltaic cell featuring a metamaterial formed from a plurality ofphotovoltaic bristles whose photovoltaic and conductive materials areconfigured to exhibit a high probability of photon absorption andinternal reflection. As a result of the high probability of photonabsorption and internal photon reflections, the metamaterial ofphotovoltaic bristles exhibits high total efficiency in converting lightenergy into electrical energy. The high total efficiency of theembodiment photovoltaic cells may lead to increased efficiency and morepower generation from the photovoltaic cell.

The various embodiments also include structural features that may resultin reduced resistance to electrical current when exposed to lightsufficient to generate electrical potentials. Such enhanced conductivitymay further efficiency and net power generated from the photovoltaiccell under certain operating conditions.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated herein and constitutepart of this specification, illustrate exemplary embodiments of theinvention, and together with the general description given above and thedetailed description given below, serve to explain the features of theinvention.

FIG. 1A is a perspective view of a number of photovoltaic bristlesextending from a substrate to form a metamaterial according to anembodiment.

FIG. 1B is a top view of the photovoltaic bristles illustrated in FIG.1A.

FIG. 1C is a cross-sectional view of a conventional photovoltaic deviceillustrating a wave front of photons.

FIG. 1D is a perspective view of photovoltaic bristles illustratingphoton interactions when an axis of the array of photovoltaic bristlesis oriented at an angle to the incident photons.

FIG. 2A is a cross-sectional top view of a section of an embodiment inwhich the photovoltaic bristles have a conductive core and two absorbersublayers or regions.

FIG. 2B is a cross-sectional side view of the photovoltaic bristlesillustrated in FIG. 2A.

FIG. 2C is a cross-sectional top view of one of the photovoltaicbristles illustrated in FIG. 2A.

FIG. 2D is a cross-sectional side view of one of the photovoltaicbristles illustrated in FIG. 2A.

FIG. 2E is a diagram illustrating off angle elements of a photon waveinteracting with a circular cross-section photovoltaic bristle.

FIG. 3A is a cross-sectional top view of a section of an embodiment inwhich photovoltaic bristles have a conductive core and three absorbersublayers or regions.

FIG. 3B is a cross-sectional side view of the photovoltaic bristlesillustrated in FIG. 3A.

FIG. 3C is a cross-sectional top view of one of the photovoltaicbristles illustrated in FIG. 3A.

FIG. 3D is a cross-sectional side view of one photovoltaic bristle ofthe photovoltaic cell illustrated in FIG. 3A.

FIG. 4A is a cross-sectional top view of a section of an embodiment inwhich photovoltaic bristles have a layered conductive core and twoabsorber sublayers or regions.

FIG. 4B is a cross-sectional side v view of the photovoltaic bristlesillustrated in FIG. 4A.

FIG. 4C is a cross-sectional top view of one of the photovoltaicbristles illustrated in FIG. 4A.

FIG. 4D is a cross-sectional side view of one of the photovoltaicbristles illustrated in FIG. 4A.

FIG. 5A is a cross-sectional top view of a section of an embodiment inwhich photovoltaic bristles have a layered conductive core and threeabsorber sublayers or regions.

FIG. 5B is a cross-sectional side view of the photovoltaic bristlesillustrated in FIG. 5A.

FIG. 5C is a cross-sectional top view of one of the photovoltaicbristles illustrated in FIG. 5A.

FIG. 5D is a cross-sectional side view of one of the photovoltaicbristles illustrated in FIG. 5A.

FIG. 6A is a cross-sectional top view of a section of an embodiment inwhich photovoltaic bristles have a semiconductor core and one absorbersublayer.

FIG. 6B is a cross-sectional side view of the photovoltaic bristlesillustrated in FIG. 6A.

FIG. 6C is a cross-sectional top view of one of the photovoltaicbristles illustrated in FIG. 6A.

FIG. 6D is a cross-sectional side view of one of the photovoltaicbristles illustrated in FIG. 6A.

FIG. 7A is a cross-sectional top view of a section of an embodiment inwhich photovoltaic bristles have a doped semiconductor core and twoabsorber sublayers or regions.

FIG. 7B is a cross-sectional side view of the photovoltaic bristlesillustrated in FIG. 7A.

FIG. 7C is a cross-sectional top view of one of the photovoltaicbristles illustrated in FIG. 7A.

FIG. 7D is a cross-sectional side view of one of the photovoltaicbristles illustrated in FIG. 7A.

FIG. 8 illustrates an embodiment method for manufacturing photovoltaiccells according to the various embodiments.

FIG. 9 is a cross-sectional side view of an array of photovoltaicbristles illustrating charge concentrations at structuraldiscontinuities, which may occur when the array is exposed to light.

FIGS. 10A-10D illustrates embodiments of the outer conductive layerincluding multiple sublayers.

FIG. 11 is a cross-sectional view of an array of photovoltaic bristlessuperimposed with an electro-magnetic field strength graphicillustrating the results of an electro-dynamics analysis of photoninteractions with the photovoltaic bristle's absorption layer using.

DETAILED DESCRIPTION

The various embodiments will be described in detail with reference tothe accompanying drawings. Wherever possible, the same reference numberswill be used throughout the drawings to refer to the same or like parts.The terms “example,” “exemplary,” or any term of the like are usedherein to mean serving as an example, instance, or illustration.References made to particular examples and implementations are forillustrative purposes, and are not intended to limit the scope of theinvention or the claims. Any implementation described herein as an“example” is not necessarily to be construed as preferred oradvantageous over another implementation.

As used herein, the term “photovoltaic bristle” refers to athree-dimensional structure approximately cylindrical with a heightapproximately equal to 1-100 microns, a diameter of approximately 0.2-50microns that includes at least one photovoltaically-active semiconductorlayer sandwiched between a conductive inner layer or core and atransparent outer conductive layer. The term “bristle” is used merelybecause the structures have a length greater than their diameter, thestructures have a generally (on average) circular cross-section, and theoverall dimensions of the structures are on the dimensions ofsub-microns to tens of microns. In the embodiment illustrated herein thephotovoltaic bristles have an approximately cylindrical, by which it ismeant that a substantial portion of the exterior surface of thestructures have a cross-section that is approximately circular orelliptical with both radii being approximately coexistent. Due tomanufacturing variability, no single photovoltaic bristle may be exactlycylindrical in profile, but when considered over a large number ofphotovoltaic bristles the average profile is cylindrical. In anotherembodiment, the photovoltaic bristles may have a non-circularcross-section, such as hexagonal, octagonal, elliptical, etc. as mayfacilitate manufacturing.

When the embodiment photovoltaic bristles are arranged on a substrate inan order or disordered array, the resulting structure may form ametamaterial structure. As used herein, the term “metamaterial” or“metamaterial substrate” refers to an array of photovoltaic bristles ona substrate. Metamaterials as used herein are artificial materials thatare engineered with metals or polymers that are arranged in a particularstructured or non-structured pattern that result in material properties(including light absorption and refraction properties) that aredifferent from the component materials. The cumulative effect of lightinteracting with the array of photovoltaic bristles may be affected bycontrolling the shape, geometry, size, orientation, material properties,material thicknesses, and arrangement of the bristles making up themetamaterial as described herein.

Traditional planar photovoltaic cells are flat. In traditional planarphotovoltaic cells, a limited number of photons are absorbed at anygiven point in time. Photon absorption occurs through the thickness ofthe traditional planar photovoltaic cell (e.g., top-to-bottom) from thepoint of photon entry until the photon is converted to electricalenergy. Traditional planar photovoltaic cells convert photons intoelectrical energy when photons interact with a photovoltaic layer.However, some photons pass through the photovoltaic layer withoutgenerating electron-hole pairs, and thus represent lost energy. Whilethe number of photons absorbed may be increased by making thephotovoltaic layer thicker, increasing the thickness increases thefraction of electron-hole pairs that recombine, converting theirelectrical potential into heat. Additionally, thicker photovoltaic filmsexhibit an exponential attenuation loss leading to a decrease in photonconversion. For this reason, traditional planar photovoltaic cells haveemphasized thin photovoltaic layers, accepting the reducedphoton-absorption rate in favor of increased conversion of electron-holepairs into electrical current and reduced heating. The theoretical peakefficiency, as well as the total efficiency, of traditional planarphotovoltaic cells is thus limited by the planar geometry and theun-attenuated fraction of photons that can be absorbed in a maximizedoptical path length through the photovoltaic layer.

Conventional planar photovoltaic cells also suffer from low totalefficiency in static deployments (i.e., without sun tracking equipment),since their instantaneous power conversion efficiency decreasessignificantly when the sun is not directly overhead (i.e., before andafter noon). Peak efficiencies of traditional planar photovoltaic cellsare affected by their orientation with respect to the sun, which maychange depending on the time of day and the season. The standard testconditions for calculating peak efficiencies of solar cells are based onoptimum conditions, such as testing the photovoltaic cells at solar noonor with a light source directly above the cells. If light strikestraditional photovoltaic cells at an acute angle to the surface (i.e.,other than perpendicular to the surface) the instantaneous powerconversion efficiency is much less than the peak efficiency. Traditionalplanar photovoltaic cells in the northern hemisphere are typicallytilted toward the south by an angle based on the latitude in order toimprove their efficiency. While such fixed angles may account for theangle of the sun at noon due to latitude, the photovoltaic cells receivesun light at an angle during the morning and afternoon i.e., most of theday). Thus, traditional planar photovoltaic cells actually result in alow total efficiency and low total power generation when measured beyonda single moment in time.

The various embodiments include photovoltaic cells that exhibitmetamaterial characteristics from regular or irregular arrays ofphotovoltaic bristles configured so the conversion of light intoelectricity occurs within layers of the photovoltaic bristles. Since thephotovoltaic bristles extend above the surface of the substrate and arespaced apart, the arrays provide the photovoltaic cells of the variousembodiments with volumetric photon absorption properties that lead toenergy conversion performance that exceeds the levels achievable withtraditional planar photovoltaic cells. The volumetric photon absorptionproperties enable the various embodiment photovoltaic cells to generatemore power than traditional planar photovoltaic cells with the samefootprint. Due to the small size of the photovoltaic bristles, thephotovoltaically-active layers within each bristle are relatively thin,minimizing power losses due to electron-hole recombination. The thinphotovoltaically-active layers help reduce attenuation losses normallypresent in thicker photovoltaic films because the photovoltaic bristlesinclude a thin radial absorption depth and a relatively thicker verticalabsorption depth maximizing photon absorption and power generation. Whenindividual photovoltaic bristles are combined in an array on, or within,a substrate, a metamaterial structure may be formed that exhibits a highprobability of photon absorption and internal reflection that leads toincreased energy conversion efficiencies and power generation. Variousembodiment structures also provide additional performance-enhancingbenefits as will be described in more detail below.

The various embodiments include configurations for positioningphotovoltaic bristles on a substrate with inter-bristle spacingsdependent on the dimensions of each bristle that trade-off shadowing andphoton absorption opportunities in order to increase the energyconversion performance. These embodiment configurations may bedetermined based upon specific dimensions, enabling a range ofphotovoltaic cell configurations depending upon the height and diameterof the photovoltaic bristles. Due to the small size of the photovoltaicbristles and the relatively short distance between bristles, the resultmay be a metamaterial in which light waves (i.e., photons when evaluatedas waves instead of particles) exhibit a higher probability ofinteracting with and being absorbed by the materials of the photovoltaicbristles than occurs with conventional photovoltaic cells. Additionallythe three-dimensional structure of the photovoltaic bristles increasesthe optical thickness of the metamaterial device. All of these factorsincrease the number of photons that are absorbed into thephotovoltaically-active layers of the photovoltaic bristles, and thusincrease the amount of light energy that is available for conversion toelectricity.

The various embodiments also include configurations of the conductiveand photovoltaically-active layers within each photovoltaic bristle interms of thickness and index of refraction that provide enhanced powerconversion performance by internally refracting photons absorbed withinthe bristles. As described in more detail below, photons may essentiallyreflect and propagate around the photovoltaic bristle's absorptionannulus thereby developing an equilibrium standing wave. Photons thatmakeup the standing wave will be absorbed and converted into an electronhole pair. This circular internally reflecting photon path and theresulting standing wave are unique to the various embodiments, and aphenomenon that cannot occur in a conventional planar photovoltaic cell.

Further performance enhancements may be obtained by positioning theembodiment photovoltaic cells so that the photovoltaic bristles are atan angle to the incident photons. This can improve the probability thatphotons will be absorbed into the photovoltaic bristles due to waveinteractions between photons and the outer conductive layer on eachphotovoltaic bristle. Orienting the embodiment photovoltaic cells at anangle to the incident photons also increases the optical depth of thephotovoltaic bristles exposed to the light, since in such an orientationthe photons strike the sides of the bristles and not just the tops. Theoff-axis photon absorbing characteristics of the photovoltaic bristlesalso enables the embodiment photovoltaic cells to exhibit significanttotal energy conversion efficiency for indirect and scattered light,thereby increasing the number of photons available for absorptioncompared to a conventional photovoltaic cell.

In a further effect resulting from the bristle-type structure of thevarious embodiments, increased amounts of current obtained from anembodiment photovoltaic cell has been found to result from decreases inthe resistance of the transparent conductive layers during insolation.This may be caused in part by electric field concentrations that candevelop at points of structural discontinuity within the arrays ofphotovoltaic bristles, which may lead to increased conductivity due tofield effects similar to what happens in field effect transistors.Analysis and observations of prototypes indicates that this reduction inresistance increases as the thickness of the outer conductive layerincreases. This decrease in resistance with decrease in outer conductivelayer thickness runs counter to conventional wisdom, which holds theopposite effect. Conventional photovoltaic cells utilize relativelythick conductive oxide layers in order to reduce power losses due toexcessive resistance in that layer. In the embodiment, thicker outerconductive layers are undesirable because they increase the minimumdiameter of the bristles and reduce the packing density within thephotovoltaic cell. Larger diameter photovoltaic bristles may exhibitlower photon absorption characteristics and reduce the photon absorbingcharacteristics of the metamaterial formed from arrays of such bristles.Thus, the observed reductions in resistance in photovoltaic bristleswith thin outer conductive layers enables the design of more efficientembodiment photovoltaic cells by enabling the use of thin outerconductive layers, which may enable smaller diameter bristles and higherpacking densities, all without increasing electrical losses due toincreases in resistance of the thinner outer conductive layer.

The compound effect of all of these energy conversion performanceimprovements is high total energy efficiency and high total powergeneration. The total energy efficiency includes a higher peakperformance at optimum conditions, but more importantly, it includes ahigher sustained average efficiency over an entire day. This means thatthe embodiment solar cells may generate more power during a day byproducing more power than conventional photovoltaic cells before andafter solar noon. Thus, with production costs expected to be onlyslightly more expensive than conventional photovoltaic cells (which havebenefited from decades of production refinements), the significantimprovement in overall energy conversion performance of the variousembodiments is expected to result in photovoltaic arrays that can becost competitive with conventional electrical power generationtechnologies, such as coal and natural gas power plants.

FIG. 1A illustrates an embodiment photovoltaic cell 100 made up of anarray of photovoltaic bristles 101 a, 101 b, 101 c, 101 d, 101 e, 101 f,101 g, 101 h, 101 i, 101 j, 101 k, 101 l, 101 m, 101 n, 101 o, 101 pextending from a substrate 102. While illustrated with twelvephotovoltaic bristles 101 a-101 p in FIG. 1A, a photovoltaic cell 100may include a large number of photovoltaic bristles, which forms ametamaterial structure. The number of photovoltaic bristles 101 on anyphotovoltaic cell 100 will depend upon the dimensions and spacing of thebristles and the size of the cell. As with conventional photovoltaiccells, individual photovoltaic cells 100 may be assembled together inlarge numbers to form panels (i.e., solar panels) of a size that aresuitable for a variety of installations.

Each photovoltaic bristle 101 a-101 p is characterized by its height“h,” which is the distance that each bristle extends from the substrate102. Photovoltaic bristles 101 a-101 p are also characterized by theirradius “r”. In an embodiment, all photovoltaic bristles 101 a-101 pwithin an array will have approximately the same height h andapproximately the same radius r in order to facilitate manufacturing.However, in other embodiments, photovoltaic bristles 101 a-101 p withinthe array may be manufactured with different height and diameters.

In an embodiment, the number of photovoltaic bristles in a photovoltaiccell may depend upon the substrate surface area available within thecell and the packing density or inter-bristle spacing. As explained inmore detail below, in an embodiment, photovoltaic bristles may bepositioned on the substrate with a packing density or inter-bristlespacing that is determined based upon the bristle dimensions (i.e., hand r dimensions) as well as other parameters, and/or patternvariations. For example, a hexagonal pattern rather than thetrigonometric pattern described, also metamaterial patterns ofvariations within the ordered arrays.

In the various embodiments, the dimensions and the inter-bristle spacingof photovoltaic bristles may be balanced against the shading ofneighboring bristles. In other words, increasing the number ofphotovoltaic bristles may increase the surface area available forabsorbing photons. However, each photovoltaic bristle casts a smallshadow, so increasing the photovoltaic bristle density of a photovoltaiccell beyond a certain point may result in a significant portion of eachbristle being shadowed by its neighbors. While such shadowing may notreduce the number of photons that are absorbed within the array,shadowing may decrease the number of photons that are absorbed by eachphotovoltaic bristle, and thus there may be a plateau in the photonabsorption versus packing density of photovoltaic bristles. A furtherconsideration beyond shadowing is the wave interaction effects of thearray of closely packed photovoltaic bristles. The interior-bristlespacing may be adjusted to increase the probability that photonsentering the array are absorbed by the photovoltaicbristles'metamaterial properties considering the bulk materialproperties of the layered films that makeup the array. For example,specific characteristics such as extinction coefficient or absorptionpath length may predict an optimal dimensional design, although one maychose to deviate from this prediction resulting in a sacrifice inperformance.

FIG. 1B shows a top view of the photovoltaic cell 100 illustrating theinter-bristle dimensions in an arbitrary arrangement of bristles. Aswill be further described below, the arrangement of bristles is shown ashaving a diamond or trapezoidal pattern, may also be any other orderedpattern (e.g., hexagonal pattern, octagonal pattern) or non-orderpattern such as a swirl. As mentioned above, each photovoltaic bristle101 a-101 p is characterized by a radius r that is measured from thecenter to the outer surface of the photovoltaic bristle 101 a-101 p. Inan embodiment, the radius r of each photovoltaic bristle 101 a-101 p maybe the same. In another embodiment, the radius r of the photovoltaicbristles may be different or vary.

In an embodiment, the array of photovoltaic bristles 101 a-101 p may beformed as rows A, B, C, D that are spaced apart on the substrate 102.While FIG. 1B illustrates just four rows of four photovoltaic bristleseach, embodiment photovoltaic cells 100 will typically include largenumbers of rows with each row including a large number of photovoltaicbristles, forming a metamaterial device.

The metamaterial configuration of the array of photovoltaic bristles,including the packing density of the photovoltaic bristles, may bedefined in terms of inter-bristle dimensions. The distance between twoneighboring photovoltaic bristles of the array of photovoltaic bristles101 a-101 p may be described by their center-to-center spacing oredge-to-edge spacing. In a regular array, the distance betweenphotovoltaic bristles may vary in different directions, so thesedistances may be referred to as the long pitch and the short pitch. Thelong pitch may be characterized in terms of the maximum center-to-centerspacing, or Long Pitch (LP) or the maximum edge-to-edge spacing, LongPitch edge-to-edge (LP_(EtoE)). The short pitch may be characterized interms of the minimum center-to-center distance or Short Pitch (SP) orminimum edge-to-edge spacing, Short Pitch edge-to-edge (SP_(EtoE)). Thecenter-to-center spacing of the photovoltaic bristles 101 may be inbetween SP and LP. In an embodiment, the array of photovoltaic bristles101 a-101 p may be formed such that the edge-to-edge spacing of allrespective neighboring photovoltaic bristles of the array ofphotovoltaic bristles 101 a-101 p may be greater than or equal toSP_(EtoE) and less than or equal to LP_(EtoE). The relationship betweeninter-bristle spacing, radii and height will be explained belowbeginning with reference to FIG. 2A.

As mentioned above, the height of the photovoltaic bristles above thesubstrate results in a metamaterial 3-D structure that exhibits greaterelectrical power generation for a given amount of insolation than can beexpected from a conventional flat photovoltaic cell of the same area.Part of this effect is due to the depth of the structure over whichphotons interact with photovoltaically-active materials. This effect isillustrated in FIGS. 1C and 1D.

As illustrated in FIG. 1C, a conventional photovoltaic cell 110 isgenerally planar with a photovoltaic active layer 111 applied to aplanar substrate 112. Due to this planar architecture, incident lightrays 120 strike a flat surface. Consequently, photon waves 122 areaccurately represented in terms of a flux, which is a measure of thenumber of photons striking an area (i.e. flat surface) per unit time.Thus, energy conversion performance of conventional photovoltaic cellsis measured against the incident photon energy measured as a flux, whichis a two-dimensional measurement. Thus, the energy conversion efficiencyof a conventional photovoltaic cell 110 is based upon the amount ofelectricity generated by unit area of the cell divided by the photonflux.

This measurement of the amount of light energy interacting withphotovoltaic cells is not necessarily appropriate for embodimentphotovoltaic cells 100 since it ignores the three-dimensional aspectresulting from the height dimension of photovoltaic bristles. This isillustrated in FIG. 1D, which shows incident light rays 120 striking thevarious surfaces presented to the light by the photovoltaic bristles101. Specifically, incident photons 120 may interact with the surface ofphotovoltaic bristles 101 along their entire length. Thus, incidentphotons interact with the embodiment photovoltaic cells 100 throughoutthe depth of the array defined by the height of the photovoltaicbristles 101. Consequently, at any given instant, the number of photonsinteracting with the embodiment photovoltaic cells 100 is equal to thenumber of photons within the volume defined by a unit area times theheight of the photovoltaic bristles 101 less the subtended anglereduction. The shadow from an eclipsing neighboring photovoltaic bristlereduces the number of photons interacting within the metamaterial andmay vary depending on the tilt of the metamaterial. Even with thesubtended angle reduction, this volumetric effect means that there aremore photons available for interacting with the photovoltaic bristles101 in embodiment photovoltaic cells 100 than is possible withconventional planar photovoltaic cells 110.

Further details of the structures making up photovoltaic bristles areillustrated in FIGS. 2A and 2B, which are cross-sectional views of aphotovoltaic cell 200 made up of an array of photovoltaic bristles 201a, 201 b, 201 c, and 201 d formed on a substrate 212. In general,photovoltaic bristles are generally cylindrical structures withgenerally cylindrical layers 203, 204 formed about a central core 206,with photovoltaically-active material layers 207 sandwiched betweenconducting materials at or on the core 206 and on the surface, which isa transparent conducting oxide layer 203. When photons interact with thephotovoltaically-active layers 207 electron-hole pairs are generated,which are conducted out of the photovoltaic bristles by the conductivelayers 206, 207 to conductive layers on the substrate 212.

The core 206 may be characterized by a core radius (r_(c)) that may bemeasured radially from the center of the photovoltaic bristle 201 b tothe inner surface of the absorption layer. The core 206 may be made of avariety of conductive materials and non-conductive materials. In anembodiment, the core 206 of a photovoltaic bristle may be a solidconductive core such as metal. For example, the core of the photovoltaicbristle may be gold, copper, nickel, molybdenum, iron, aluminum, dopedsilicon, and silver. In other embodiments, the core of a photovoltaicbristle may made from a non-conductive center, such as a semiconductoror polymer plastic, that is coated or covered with a conductive layer,such as gold, copper, nickel, molybdenum, iron, aluminum, doped silicon,or silver. In an embodiment, the core 206 may also include a coating tostrengthen the microstructure 201 b. In a further embodiment, the coreof the photovoltaic bristles may the made from a doped semiconductormaterial, such as p-type amorphous silicon or n-type amorphous silicon.In another embodiment, the core 206 may be made from a differentmaterial than the substrate 212. In an embodiment, the core 206 may bemade from the same material as the substrate 212.

The photovoltaic bristle includes an absorption layer 207 made up of oneor more sublayers 204, 205 of photovoltaically-active materials that areconfigured to generate electron-hole pairs when a photon is absorbed. Inan embodiment, the absorption layer 207 may include a p-typesemiconductor sublayer (204 or 205) and an n-type semiconductor sublayer(205 or 204) forming a p-n junction within the absorption layer 207. Forexample, the p-type and the n-type semiconductor sublayers may beappropriately doped amorphous silicon. In another embodiment, theabsorption layer 207 may include a p-type semiconductor sublayer, anintrinsic semiconductor sublayer, and an n-type semiconductor sublayer.For example, the p-type semiconductor, the intrinsic semiconductor, andthe n-type semiconductor sublayers may be amorphous silicon. In afurther embodiment, the absorption layer 207 of a photovoltaic bristlemay be a single doped semiconductor sublayer forming a p-n junction withthe core 206 that is doped to be either a p- or n-semiconductor. Forexample, in this embodiment the core 206 may be a p-type semiconductorand the absorption layer 207 may an n-type semiconductor layer.

As mentioned above, embodiment photovoltaic cells may be configured withbristle-packing densities defined according to the materials anddimensions of the photovoltaic bristles. As mentioned above,photovoltaic bristles 201 a-201 d have a radius r measured from thecenter of the photovoltaic bristle to the outer perimeter of thephotovoltaic bristle. For purposes of calculating the bristle packingdensity, the mean radius r_(m) of the bristles may be used since theindividual radii may vary due to the variability of manufacturingtechniques.

Each photovoltaic bristle 201 a-201 d is made up of a core 206 that isconductive or has a conductive outer surface, absorption layer 207, andan outer conductive layer 203, which will typically be transparentconductive layer such as a transparent conductive oxide or transparentconductive nitride. Due to the cylindrical form of photovoltaicbristles, the absorption layer 207 surrounds the core 206, and the outerconductive layer 203 surrounds the absorption layer 207. The absorptionlayer 207 as radial thickness (d_(abs)) that may be measured radiallyfrom the outer surface of the core 206 to the inner surface of the outerconductive layer 203. The absorption layer 207 may include a number ofabsorber sublayers or regions of photovoltaically-active materials orcombinations of photovoltaic materials. For example, the absorptionlayer 207 may include multiple absorber sublayers or regions that form ap-n junction, a p-i-n junction, or multi-junction regions, which have agenerally circular cross-section as illustrated in FIG. 2A. The absorbersublayers or regions 204, 302, 205 may be made from one or more ofsilicon, amorphous silicon, polycrystalline silicon, single crystalsilicon, cadmium telluride, gallium arsenide, aluminum gallium arsenide,cadmium sulfide, copper indium selenide, and copper indium galliumselenide.

The relative radial positions of the p-type, intrinsic, or n-typesublayers/regions may vary in the embodiments. For example, in oneembodiment the p-type semiconductor material may be positioned radiallyinside the n-type semiconductor material. In another embodiment, then-type semiconductor material may be positioned radially inside thep-type semiconductor material. In addition, multiple materials may beused to create a sequence of p-n and/or n-p junctions, or p-i-njunctions in the absorption layer. For example, the absorption layer mayinclude an absorber sublayer of p-type cadmium telluride (CdTe) and anabsorber sublayer of n-type cadmium sulfide (CdS). In an embodiment, theabsorption layer 207 may be fully depleted. For example, the p-typeregion and the n-type region forming the sublayer or region 204 and thesublayer or region 205 may be fully depleted.

In an example embodiment, the absorption layer 207 may include a p-typesemiconductor sublayer 205, such as p-type cadmium telluride, and ann-type semiconductor sublayer of a different material, such asn-type-cadmium sulfide. In another example embodiment, one sublayer 204may be a p-type region, such as p-type amorphous silicon, and anothersublayer 205 may be an n-type region of the same material as thesublayer 204 but doped to form an n-type semiconductor, such as n-typeamorphous silicon.

For purposes of illustration, the absorption layer 207 radial thickness(d_(abs)) may encompass all the absorber sublayers or regions. Invarious embodiments, the absorption layer 207 thickness (d_(abs)) may beless than 0.01 microns, approximately 0.01 microns, or greater than 0.01microns. Embodiment absorber thickness (d_(abs)) ranges include 0.01 to0.10 microns, 0.10 to 0.20 microns, 0.20 to 0.30 microns, 0.30 to 0.40microns, 0.40 to 0.50 microns, 0.50 to 0.60 microns, 0.60 to 0.70microns, 0.70 to 0.80 microns, 0.80 to 0.90 microns, 0.90 to 1.0microns, 0.01 to 1.0 microns, and more than 1.0 microns. In an exampleembodiment, the absorption layer 207 thickness (d_(abs)) may beapproximately 0.64 microns subject to variability in the manufacturingprocess by which the absorption layers are applied to the core 206.

The outer conductive layer 203 has a radial thickness (d_(ocl)) whichmay be measured radially from the outer surface of the absorption layer207 to the outer surface of the outer conductive layer 203 (i.e., theouter surface of the photovoltaic bristle). In an embodiment, the outerconductive layer 203 is a transparent conductive oxide (“TCO”), such asa metal oxide. In an embodiment, the outer conductive layer 203 mayinclude a dopant creating a p-type or n-type transparent conductiveoxide. For example, the transparent conductive oxide layer 203 may beone of intrinsic zinc oxide, indium tin oxide, and cadmium tin oxide(Cd₂SnO₄). In an embodiment, the outer conductive layer 203 may includea transparent conductive nitride such as titanium nitride (TiN). Inanother embodiment, the outer conductive layer 203 may include a bufferwith or without the dopant. Some examples of an outer conductive layer203, which may be a transparent conductive oxide with a dopant, includeboron doped zinc oxide, fluorine doped zinc oxide, gallium doped zincoxide, and aluminum doped zinc oxide. Some examples of buffers that maybe added to a transparent conductive oxide include zinc stannate(Zn₂SnO₄), titanium dioxide (TiO₂), and similar materials well known inthe art.

As shown and described later with FIGS. 10A-10D, the outer conductivelayer 203 may include a number of multiple conductive and/ornon-conductive sublayers to allow a photovoltaic bristle to meet therequired design optical thickness (d_(ocl)) while simultaneouslybenefiting from the field effects generated from a thin transparentconductive sublayer within the outer conductive layer 203. With multiplesublayers, the outer conductive layer 203 may also benefit from addedflexibility to the photovoltaic bristles for a more resilientmetamaterial device. As an example, a bi-layer outer conductive layer203 may include a conductive sublayer such TCO and a non-conductivesublayer such as an optically transparent polymer.

As shown in FIG. 2B, the photovoltaic bristles extend from a substrate212 of the photovoltaic cell 200. The substrate 212 may be any suitablesubstrate material known in the art. For example, the substrate 212 maybe glass, doped semiconductor, diamond, metal, a polymer, ceramics, or avariety of composite materials. The material used in the substrate 212may be a material used elsewhere in the photovoltaic cell 200, such as amaterial used in any layer of a photovoltaic bristle 201 a-201 d.Alternatively, the material used in the substrate 212 may be differentfrom the materials in the photovoltaic bristles 201 a-201 d. In anembodiment, the core 206 and the substrate 212 may be made from the samebase material that is covered by a conductive material. For example, thesubstrate 212 and the cores 206 may be made from glass, semiconductormaterial, a polymer, ceramics, or composites. In a further embodiment,the core 206 and substrate 212 may include similar materials, while thecore 206 is made from additional materials, such as gold, copper,nickel, molybdenum, iron, aluminum, or silver.

In the various embodiments, the index of refraction of the outerconductive layer 203 and absorption layer 207 and sublayers 204, 205 aswell as the thicknesses of these layers may be configured to increasethe probability of absorption of incident photons and internalrefraction of absorbed photons as illustrated in FIGS. 2C and 2D. Asillustrated in FIG. 2C, photovoltaic bristles 201 designed and formed inaccordance with the embodiment designs described below, may guide anabsorbed photon 210 so that it follows an internal path 211 thatexhibits a high probability that the photon remains within thephotovoltaic bristle 201 due to total internal reflection. Asillustrated, by adjusting the index of refraction and thickness of eachlayer 203, 204, 205, a photon may be caused to refract inwardly until itcontacts the conductive core 206 where it may be spectrally reflected.It should be noted that the embodiment illustrated in FIGS. 2A-Dfeatures and inner reflector due to the metal core 206. In otherembodiments described herein, a refraction layer may be applied over thecourt (core) 206 to achieve the same photon reflection effects. In suchan embodiment, a reflective layer may be formed over the conductive coreand under the absorber layer, such as a semiconductor or dielectricmaterial layer having a lower index of refraction than the absorberlayer. This refraction layer may be configured to reflect the photon atthe interface between the reflection layer and the absorber layer, andnot rely on reflection off of the conductive core 206. For example, sucha diffraction layer may be formed from an aluminum doped zinc oxidelayer of about 500-1500 angstroms in thickness. Reflected photons thenrefract through each layer 204, 205 until they reach the outerconductive layer 203, where the difference in the index of refractionbetween the absorption sublayer 205 and the outer conductive layer 203causes the photons to reflect back into the absorption layers of thephotovoltaic bristle. Those reflected photons that are not reflectedinwardly at the boundary between the outer conductive layer 203 and theabsorption sublayer 205 may pass through the outer conductive layer 203and be reflected off of the interface between the outer conductive layer203 and air due to the difference in the index of refraction at thisinterface. In either manner, photons may remain within the photovoltaicbristle passing back and forth through the absorption layer 207 untilthey are eventually absorbed or exit the bristle.

FIG. 2D illustrates the photon traveling within and around thephotovoltaic bristle 201. Since the photovoltaic bristle 201 extends adistance h above the substrate, a photon 210 entering the bristle at anangle may travel along the axial length or height of the photovoltaicbristle 201.

FIG. 2D also illustrates that photons striking the photovoltaic bristle201 will have a higher probability of absorption when they strike thesidewall of a photovoltaic bristle at a compound angle that is less than90 degrees but more the 0 degrees to the surface, where an angleperpendicular to the sidewall surface is considered to be 0 degrees. Thecompound incident angle includes a vertical plane component 233 (shownin FIG. 2D) and a horizontal plane component 232 (shown in FIG. 2C). Thehorizontal plane component 232 is defined by a photon 210 striking theouter surface of the bristle at a point along the perimeter of thecircular cross-section plane forming an angle with the perimeter wherean angle perpendicular to the perimeter is considered 0 degrees.Similarly, the vertical plane component 233 is defined by the photon 210striking the outer surface of the bristle at a point along the heightforming a vertical angle with the surface where an angle perpendicularto the surface is considered 0 degrees. Analysis of photon absorptioncharacteristics of the outer conductive layer revealed that photonsstriking the surface of the sidewall of the photovoltaic bristle atnormal in the horizontal component 232 and the vertical component 233may result in a compound angle of 0 degrees and a high probability ofbeing reflected off the surface. Similarly, photons striking the surfaceof the sidewall of the photovoltaic bristle parallel to the vertical andthe horizontal component will also have a high probability of beingreflected off the surface. However, photons striking the side surface ata compound angle between 10° and 80° have a high probability of beingabsorbed into the outer conductive layer 203. Once absorbed, theinternal refraction characteristics of the absorption layers 204, 205and outer conductive layer 203 cause the photons to remain within thephotovoltaic bristle 201 for an extended time or path length. Thischaracteristic is very different from conventional photovoltaic cells,which exhibit the maximum power conversion efficiency when the angle ofincidence of photons is normal to its single planar surface.

The difference between the incident angle corresponding to conventionalphotovoltaic cells and the photovoltaic bristles is illustrated by angleθ_(p) in FIG. 2D. The preferred incident angle for a traditional solarcell, θ_(p), would form a right angle with the top of the bristle aswell as the substrate of the full metamaterial device (not shown). Thus,not only does the photovoltaic bristle exhibit better absorptioncharacteristics at off-angles (not perpendicular or parallel to thesurface), the reference point for measuring an off-angle is vastlydifferent from a conventional photovoltaic cell. For a metamaterialdevice with photovoltaic bristles, the reference point is measured fromthe sidewall of a bristle in two planes, which is unachievable by aplanar photovoltaic cell. Thus, due to the off-angle absorptioncharacteristics of photovoltaic bristles, the embodiment photovoltaiccells exhibit significant power conversion efficiency across a broadrange of angle of incidence. This translates to more power generationthroughout the day than achievable from fixed solar panels withconventional planar solar arrays that produce their peak efficiencies(i.e., maximum power generation) when the sun is directly overhead.

Although conventional planar solar arrays may have high peak efficiency,as described above, peak efficiencies are only a single point in time.Typically conventional planar photovoltaic cells show a significant dropin efficiency and power generation in the morning and the afternoon(i.e., not solar noon). Due to the drop in efficiency, the conventionalphotovoltaic cells have a low total efficiency (or average efficiency)when measured over an entire day leading to a low total powergeneration. However, the embodiment metamaterials with photovoltaicbristles have sustained high efficiency throughout the day because thecompound angle of incidence for the metamaterial more closely mirrorsthat of sun's presentation of photons. Thus, photons are more likely tostrike the sidewalls of the photovoltaic bristles 201 with a compoundangle of incidence between approximately 10 and 80 degrees resulting insustained high absorption efficiency and a high total power generation.

While photovoltaic bristles absorb photons more readily when they strikethe surface at an angle, the probability of photon absorption is not astrong function of angle of incidence. This is due to the small diameterand circular cross-section of photovoltaic bristles and the wave natureof photons. As illustrated in FIG. 2E, even a photon 210 striking thesurface of a photovoltaic bristle 201 at a right angle 220 to thesurface will interact with the surface at smaller angles of incidencedue to the wave nature of the photon. As illustrated, a photon 210 has awave function that extends beyond its line of travel 211 such that thereis a probability of the photon interacting with the surface of thephotovoltaic bristle 201 some distance from the intersection of the lineof travel. Due to the small diameter and circular nature of the bristle,there is a finite probability that the photon will interact with thesurface at a smaller angle 222 on either side of the line of travel 211.It is also a finite probability that the photon will interact with thesurface at even smaller angles 224, 226 a further distance from the lineof travel 211. Thus, even a photon that might be expected to bereflected from a photovoltaic bristle has a significant probability ofbeing absorbed due to the interaction of the photon wave with the curvedsurface of the bristle.

As described above, the materials and thicknesses forming the outerconductive layer and absorption layers of the photovoltaic bristle maybe selected to result in a high probability of photon internalrefraction to increase the probability of photon absorption. This mayinclude selecting materials so that the index of refraction of outertransparent conducting oxide layer (n_(ocl)) is lower than the index ofrefraction of the inner absorption layers. For, example the index ofrefraction of the outer conductive layer may be lower than the index ofrefraction of the absorption layer. In addition, the index of refractionof outer transparent conducting oxide layer (n_(ocl)) will be greaterthan the index of refraction of air (n_(air)). Thus, the materials ofmaterials and thicknesses forming the outer conductive layer andabsorption layers may be selected so that each layer moving inward has ahigher index of refraction than the preceding outer layer and all layersmay have greater indexes of refraction than air.

By radially ordering the materials by indexes of refractions from a lowindex of refraction on the outside to a higher index of refraction ineach inner layer, the photovoltaic bristle 201 may refract or guidephotons 210 towards the core 206 of the photovoltaic bristle 201. Sincethe core 206 is highly conductive, it is also highly reflective, so thatit will reflect photons 210. Due to the large difference in index ofrefraction between the absorber layer and the outer conductive layer203, photons striking this boundary at an angle will be refractedinwardly. As a result of these reflections and refractions, photons 210may be effectively trapped within the absorption layer 207 for a longerperiod of time, thereby increasing the probability of interaction withthe absorption layer 207 causing an electron-hole pair to be formed.Increasing the probability of photon absorption may result in moreelectrical current being generated for the same amount of incident lightenergy by the embodiment photovoltaic cells than is achievable byconventional photovoltaic cells.

In an embodiment mentioned above, an inner refraction or reflectionlayer may be added on top of the core 206 in order to provide an innerreflection interface for photons. In this embodiment, a layer ofsemi-conductive or insulator material, such as Al:ZnO, ZnO, or ITO, maybe applied over the metal core. This layer may be at least one-halfwavelength in thickness, depending on the refractive index of thematerial. For example, such a layer made of Al:ZnO (AZO) may beapproximately 1500 angstroms thick over which the absorber layer may beapplied. Such an AZO layer has a refractive index that is lower than theabsorber layer. This difference in refractive index coupled with thecurvature of the interface of these two layers will reflect the photonsbefore they reach the metal core. The reflection induced by this designmay exhibit lower losses than then designs in which photons reflect froma metal surface of the core. This additional refraction layer over thecore may be included in the equations for determining the photovoltaicbristle diameter as a contributor to the r_(c) value. In other words,including a 1500 angstrom AZO layer over a 0.75 micron radius core wouldresult in a core diameter r_(c) for purposes of the design equations of0.9 microns. The use of such a refraction layer may be included in anyof the embodiments illustrated and described herein. For example, in theembodiments in which the center of the core is a plastic rod, a metallayer is applied over the plastic core and then the AZO is applied overthe metal layer. In further embodiments, this refractive layer forming areflecting interface may be formed using multiple layers, such as:ITO-AZO; ITO-AZO-ITO; TiO2-TiN—TiO2; ZnO-AZO—ZnO; etc. Such multiplelayer may function similar to a Bragg reflector used in fiber optics.

The higher energy conversion efficiency enabled by photovoltaic bristlesof the various embodiments may be achieved by designing the bristleswith outer conductive layer and absorption layer materials andthicknesses, with the bristles spaced apart at a packing density thatoptimize or nearly optimize the performance enhancement characteristicsdescribed above. This may be achieved by designing the photovoltaicbristles and arranging the arrays of the bristles using the followingdesign techniques.

In an embodiment, the outer conductive layer and absorption layermaterials and thicknesses of photovoltaic bristles may be selected inset according to equation 1:

$\begin{matrix}{\frac{n_{ocl}*r_{c}}{n_{air}*\left( {r_{c} + d_{abs} + d_{ocl}} \right)} \leq 1} & {{Eq}.\mspace{14mu} 1}\end{matrix}$where:

r_(c) is the bristle core radius;

n_(air) is the index of refraction for air;

n_(ocl) is the index of refraction of the outer conductive layer;

d_(ocl) is the thickness of the outer conductive layer; and

d_(abs) is the thickness of the absorption layer.

The median radius of a photovoltaic bristle (r_(m)) is set according toequation 2:r _(m) =r _(c) +d _(abs) +d _(ocl)  Eq. 2where:

r_(m) is the median radius of the photovoltaic bristles. Thus, themedian radius of a photovoltaic bristle (r_(m)) is the sum of thebristle's core radius (r_(c)) and the thicknesses of the absorptionlayer (d_(abs)) and outer conductive layer (d_(ocl)).

Combining equation 1 and equation 2 and solving for the median radius ofthe photovoltaic bristles (r_(m)) yields equation 3:

$\begin{matrix}{r_{m} \geq \frac{n_{ocl}*\left( {d_{abs} + d_{ocl}} \right)}{\left( {n_{ocl} - n_{air}} \right)}} & {{Eq}.\mspace{14mu} 3}\end{matrix}$

Thus, the radius (r_(m)) of the photovoltaic bristles may depend uponthe first radial thickness (d_(abs)), the second radial thickness(d_(ocl)), the index of refraction of the outer conductive layer(n_(ocl)), and the index of refraction of air (n_(air)). In other words,a photovoltaic bristle with a ratio as defined in equation 3 willexhibit a high probability of photon internal refraction, and thusexhibit a higher probability of photon absorption and electron-holegeneration

Equation 3 may also be used to calculate the appropriate thicknesses forthe outer conductive layer and absorption layer, since these two layerthicknesses are related in the equation. In order to increase the amountof photovoltaic material, the absorption layer thickness (d_(abs)) maybe set to be greater than the outer conducting layer radial thickness(d_(ocl)). However, the outer conductive layer will need to have aminimum thickness in order to maintain desirable conductivity. Thus,there will be a design balance between the two layer thicknesses. In anembodiment, the transparent conducting oxide layer thickness (d_(ocl))may be about two thirds (i.e., approximately sixty-seven percent) of theabsorption layer thickness (d_(abs)). Thus, in this embodiment, theouter conductive layer thickness (d_(ocl)) may be determined by equation4:d _(ocl)=0.67*d _(abs)  Eq. 4For example, with an absorption layer thickness d_(abs) of approximately0.64 microns, the outer conductive layer thickness, d_(ocl), would beapproximately 0.43 microns. Although the outer conductive layer may bedetermined by equation 4, the actual thickness of the outer conductivelayer may deviate from this relationship. The actual thickness of theouter conductive layer may be thicker, but thicker outer conductivelayers may result in a higher probability that photons will graze offthe outer conductive layer instead entering the absorption layer. Thus,equation 4 is merely an exemplary relationship between the thicknessesof outer conductive layer and the absorption layer.

It is worth noting that the radius of the bristle r_(m) as defined byequation 2 is important for considerations of inter-bristle spacing inorder to address shading issues since thicker bristles cast widershadows. The core radius r_(c) is also a key consideration, particularlyfor manufacturability and for structural rigidity considerations. Whiletall thin bristles may be desirable for energy conversion efficiencyreasons, there is likely to be a minimum core radius below whichphotovoltaic bristles cannot be affordably manufactured. Thus, thebristle core radius r_(c) parameter may be determined based upon thetype of manufacturing process used to create them. The bristle coreradius r_(c) parameter may also be determined based upon the strengthproperties of the material used to form the cores. Stronger materialsmay enable the bristles to be made smaller in diameter (i.e., with asmaller core radius r_(c)). On the other hand, weaker materials that mayenable lower cost or higher product rates may require the bristles to bemade larger in diameter (i.e., with a larger core radius r_(c)).

As mentioned above, a photovoltaic cell 200 including an array ofphotovoltaic bristles may be designed to achieve high power generationefficiency by reducing the shading of neighboring bristles in the array.The shading caused by neighboring bristles may be reduced by controllingthe minimum edge-to-edge spacing (SP_(EtoE)) and maximum edge-to-edgespacing (LP_(EtoE)) between photovoltaic bristles. In an embodiment, theminimum edge-to-edge spacing (S_(PEtoE)) may be calculated usingequation 5:SP_(EtoE)=((1.67*d _(abs))+r _(c))*(2)*(0.9)  Eq. 5where (r_(c)) is the core radius (e.g., radius of core 206 ofphotovoltaic bristle 201 b as illustrated in FIG. 2A), and (d_(abs)) isthe thickness of the absorption layer (e.g., thickness of the absorptionlayer 207). For example, for a bristle having an absorption layerthickness (d_(abs)) of 0.64 microns and a core radius (r_(c)) of 0.75microns, the minimum edge-to-edge spacing (SP_(EtoE)) would beapproximately 3.27 microns. In this embodiment, the array ofphotovoltaic bristles may be formed so that no two neighboring bristlesin the array are closer than approximately 3.27 microns.

The maximum edge-to-edge spacing (LP_(EtoE)) between photovoltaicbristles may be calculated using equation 6:LP_(EtoE)=((1.67*d _(abs))+r _(c))*(2)*(1.1)  Eq. 6For example, for photovoltaic bristles having an absorption layerthickness (d_(abs)) of 0.64 microns and a core radius (r_(c)) of 0.75microns, the maximum edge-to-edge spacing (LP_(EtoE)) would beapproximately 4.0 microns. In this embodiment, the array of photovoltaicbristles may be formed so that no two neighboring bristles in the arrayare separated by more than 4.0 microns. Although the maximum spacing isgiven by the example equation 6, bristles may have a larger edge-to-edgespacing than the limits of the equation. However, increasing theedge-to-edge spacing beyond the maximum provided in equation 6 mayresult in less power generation, due to the lower number of bristles inthe metamaterial device.

Equations 4 and 5 may be combined to define the overall edge spacing ofneighboring photovoltaic bristles to define the range of edge-to-edgespacing (P_(EtoE)) for neighboring photovoltaic bristles as shown inequation 7:((1.67*d _(abs))+r _(c))*(2)*(0.9)≦P _(EtoE)≦((1.67*d _(abs))+r_(c))*(2)*(1.1)  Eq. 7

As an example, photovoltaic bristles with an absorption layer thickness(d_(abs)) of 0.35 microns and a core radius (r_(c)) of 0.6 microns wouldbe arranged with a minimum edge-to-edge spacing (SP_(EtoE)) ofapproximately 2.13 microns and a maximum edge-to-edge spacing(LP_(EtoE)) of approximately 2.61 microns. Designing photovoltaicbristles according to equation 1 and designing the array spacing ofphotovoltaic bristles according to equation 7 may result in ametamaterial device according to the various embodiments that exhibitssignificantly higher energy conversion efficiencies than is achievablewith conventional photovoltaic panels.

It is worth noting that the arrays of bristles within the metamaterialmay be ordered or non-ordered. An ordered array of bristles may have adefined geometric pattern as limited by the trigonometric values such asthe short edge-to-edge and long edge-to-edge spacing provided inequation 7. However, the ordered arrays may include a hexagonal patterninstead of a strict trigonometric pattern meaning that the maximumedge-to-edge spacing of a neighboring bristle neighbor spacing may begreater than that listed in equation 6. The ordered array of bristlesmay also include a diamond pattern, a rectangular pattern, a pentagon,octagon or any other geometric pattern. In an embodiment, the arrays ofbristles may be a non-ordered pattern. The non-ordered pattern ofbristles may be created similar to the ordered-pattern, such as atrigonometric pattern as described in the equations above, but alsoincluding a break in the pattern. For example, the bristles may have astandard trigonometric pattern, but every fifth bristle in a row isremoved. Alternatively, the metamaterial may include any non-standardgeometric pattern for the bristle arrangement such as a swirlingarrangement of bristles.

The height of each photovoltaic bristle within the array of photovoltaicbristles may also affect the probability of photon absorption. In anembodiment, the height of a photovoltaic bristles may be greater than0.1 microns and less than or equal to 100 microns. In an embodiment, theheight of a photovoltaic bristle may be selected based on othercharacteristics of the array of photovoltaic bristles, including thecore radius of each photovoltaic bristle and the spacing betweenphotovoltaic bristles. In part, this selection of the bristle height ismade based on the bristle diameter and separation distances to ensurethat at least a portion of the bristle sidewall is not shadowed byadjacent bristles. This design consideration is a matter of simplegeometry once the bristle core radius and separation distances areselected. As described above, the bristle radius and spacing distancesmay be determined based upon material indices of refraction andthicknesses of the absorption layer and transparent conducting oxidelayer, and the bristle core radius, each of which may be defined orselected based on the properties of the materials used for these partsof the photovoltaic bristle. Thus, bristle height may also be determinedbased on those properties and thicknesses. In short, the entire size andspacing of the photovoltaic bristles in an embodiment photovoltaic cellmay be determined by the material properties of the bristle core,absorption layers and transparent conducting oxide.

The energy conversion efficiency embodiment photovoltaic cells made upof an array of photovoltaic bristles may be increased by designing thephotovoltaic bristles with a minimum height (h_(min)) that is determinedbased on the bristle radius and separation distances using equation 7:

$\begin{matrix}{h_{\min} = \frac{\left( {\left( {\left( {1.67*d_{abs}} \right) + r_{c}} \right)*(2)*(0.9)} \right)}{\tan\left( {40{^\circ}} \right)}} & {{Eq}.\mspace{14mu} 7}\end{matrix}$where r_(c) is the radius of the core, and d_(abs) is the thickness ofthe absorption layer. For example, with a core radius (r_(c)) of 0.75microns and an absorption layer thickness (d_(abs)) of 0.64 microns, andthe minimum height for the microstructure may be 3.90 microns. In Eq. 7the term tan(40°) is provided as a design guideline for mostapplications. However, this factor may be replaced with the tangent ofany angle up to approximately 80 degrees. The result of increasing theangle would be taller bristles. The angle selected in this equation maybe adjusted for integrated power gain optimization. This angle may alsochange depending on whether the photovoltaic cell will be used fortracking or non-tracking designs.

With the seven design formulas described above, a range of embodimentphotovoltaic cell designs can be developed that exhibit the desirableenergy conversion efficiency characteristics described above. Forexample, FIGS. 2A-2D illustrate an embodiment in which the absorptionlayer 207 is made up of to sublayers 204, 205, such as a p-typesemiconductor layer and an n-type semiconductor layer to produce a PNjunction absorption layer 207. The embodiment illustrated in FIGS. 2A-2Dfeatures a solid conductive core 206, such as a core made from a metal,metal alloy or conductive semiconductor as listed above. However,photovoltaic bristles may also be made with more sublayers, as well asnon-conductive cores provided a conductive coating is applied to thecore before photovoltaic material layers are applied. Other exampleembodiments of photovoltaic cell designs are described below withreference to FIGS. 3A-3D, 4A-4D, 5A-5D, 6A-6D, and 7A-7D.

FIGS. 3A, 3B, 3C, and 3D illustrate an embodiment photovoltaic cell 300in which the absorption layer 207 in the photovoltaic bristles 201 a-201d include three absorber sublayers or regions 204, 302, 205. In anembodiment, the absorption layer thickness (or a first radial thickness)(d_(abs)) is equal to the thicknesses of the three absorber sublayers orregions 204, 302, 205 combined. In an embodiment, the absorber sublayers204, 302, 205 may be a n-type semiconductor material, an intrinsicsemiconductor material, and a p-type semiconductor material,respectively. In an alternative embodiment, the absorber sublayers maybe arranged in the reverse order, such that absorber sublayers 204, 302,205 may be a p-type semiconductor material, an intrinsic semiconductormaterial, and a n-type semiconductor material. In another embodiment,the absorber sublayers 204, 302, 205 may be a p-type semiconductor, ann-type semiconductor, and a p-type semiconductor, respectively. In anembodiment, the absorber sublayers 204, 302, 205 may be a n-typesemiconductor, a p-type semiconductor, and a n-type semiconductor,respectively. In an embodiment, the absorption layer may includemultiple p-n or p-i-n junctions.

In various embodiments, the absorber sublayers or regions 204, 302, 205may made from one or more of silicon, amorphous silicon, polycrystallinesilicon, single crystal silicon, cadmium telluride, gallium arsenide,cadmium sulfide, copper indium selenide, and copper indium galliumselenide. In an embodiment, the semiconductor materials for eachabsorber sublayer 204, 302, 205 may be different semiconductormaterials. In an embodiment, the semiconductor materials for eachabsorber sublayer 204, 302, 205 may be the same semiconductor material.For example, absorber regions 204, 302, 205 may include a n-typeamorphous silicon, an intrinsic amorphous silicon, and a p-typeamorphous silicon.

In an embodiment, the materials of the various layers may be selected sothat the index of refraction of the outer conductive layer (n_(ocl)) isgreater than the index of refraction of air (n_(air)), the index ofrefraction of the outer conductive layer (n_(ocl)) is less than theindex of refraction of the first absorber sublayer 204, the index ofrefraction of the first absorber sublayer 204 is less than the index ofrefraction of the third absorber sublayer 302, and the index ofrefraction of the third absorber sublayer 302 is less than the index ofrefraction of the second absorber sublayer 205. In an alternateembodiment, the materials of the various layers may be selected so thatthe index of refraction of the outer conductive layer (n_(ocl)) is lessthan the index of refraction of the absorption layer 207 which is madeup of the three absorber regions 204, 302, 205. As described above, byselecting the layer materials so that there indices of refractions veryfrom a low index of refraction on the outside to a higher index ofrefraction in each layer moving radially inward, the photovoltaicbristle 201 b may refract or guide photons 210 toward the core 206 ofthe photovoltaic bristle 201 b as illustrated in FIGS. 3C and 3D.

FIGS. 4A, 4B, 4C, and 4D illustrate an embodiment photovoltaic cell 400featuring photovoltaic bristles with to sublayers 204, 205 within theabsorption layer 207 (similar to the embodiment described above withreference to FIGS. 2A-2D), in which the cores of the photovoltaicbristles may be in the form of a non-conductive center core 403 that iscovered by a conductive layer 402. For ease of reference, the conductivelayer 402 over the non-conductive center core 403 is referred to hereinas the “inner conductive layer” in order to distinguish it from thetransparent conducting oxide layer 203, which may be referred to as the“outer conductive layer.” In this embodiment, the radius of the core(r_(c)) may be measured from the center of the non-conductive center 403to the outer surface of the inner conductive layer 402.

In an embodiment, the inner conductive layer 402 may be a metal or metalalloy, such as gold, copper, nickel, molybdenum, iron, aluminum, silveror alloys of the same. In an embodiment, the non-conductive center 403may include a polymer, glass, a composite material, or a semiconductormaterial.

The embodiment illustrated in FIGS. 4A, 4B, 4C, and 4D may exhibitenergy conversion performance characteristics that are similar toembodiments featuring a solid conductive core when designed according tothe embodiment methods described above, with the added benefit ofenabling the use of less-expensive or easier to process materials forthe bristle cores. For example, this embodiment would enable productionof photovoltaic bristles with plastic or polymer cores, such as could bemanufactured using stamping, pressing or molding techniques. While usingsuch materials may require adjustments in the diameter of the core inorder to achieve desirable manufacturing yields, the embodiment designmethods described above enable the design of embodiment photovoltaiccells with similar performance characteristics.

FIGS. 5A, 5B, 5C, and 5D illustrate an embodiment photovoltaic cell 500in which the absorption layer 207 in the photovoltaic bristles 201 a-201d include three absorber sublayers or regions 204, 302, 205, andnon-conductive core centers 403 covered with an inner conductive layer402 is described above. Thus, this embodiment is an example of acombination of the embodiments described above.

FIGS. 6A, 6B, 6C, and 6D illustrate an embodiment photovoltaic cell 600in which the absorption layer 207 of photovoltaic bristles comprises asingle layer and the core 206 comprises a semiconductor. In thisembodiment, the semiconductor core 206 may be made from a p-type orn-type semiconductor material so that the junction of the absorptionlayer 207 and the semiconductor core 206 form a p-n junction suitable toconvert photons into electro-hole pairs.

In an embodiment, the semiconductor core 206 may be a p-typesemiconductor material and the absorber sublayer 207 may be a n-typesemiconductor material. Alternatively, the semiconductor core 206 may bea n-type semiconductor material and the absorber sublayer 207 may be ap-type semiconductor material. In an embodiment, the semiconductormaterial for the core 206 and the absorber sublayer 207 may be differentmaterials. For example, the semiconductor core 206 may be p-type cadmiumtelluride and the absorber sublayer 207 may be n-type cadmium sulfide.As another example, the semiconductor core 206 may be n-type cadmiumsulfide and the absorption layer 207 may be p-type cadmium telluride.

In another embodiment, the semiconductor materials for the semiconductorcore 206 and the absorber sublayer 207 may be the same semiconductormaterials. For example, the semiconductor core 206 may include a p-typeamorphous silicon and the absorber sublayer 207 may include a n-typeamorphous silicon. Alternatively, the semiconductor core 206 may includea n-type amorphous silicon and the absorber sublayer 207 may include ap-type amorphous silicon. The semiconductor core 206 may made from oneor more of silicon, amorphous silicon, polycrystalline silicon, singlecrystal silicon, cadmium telluride, gallium arsenide, aluminum galliumarsenide, cadmium sulfide, copper indium selenide, and copper indiumgallium selenide. The absorber sublayer 207 may be made from one or moreof silicon, amorphous silicon, polycrystalline silicon, single crystalsilicon, cadmium telluride, gallium arsenide, aluminum gallium arsenide,cadmium sulfide, copper indium selenide, and copper indium galliumselenide.

FIGS. 7A, 7B, 7C, and 7D illustrate an embodiment photovoltaic cell 700in which the core 206 of the photovoltaic bristles is made from asemiconductor, and the absorption layer 207 is made up of two absorbersublayers 204, 205, the inner layer of which combines with thesemiconductor core 206 so that a p-i-n junction is formed. In anembodiment, the semiconductor core 206, the absorber sublayer 205,absorber sublayer 204 may be a p-type semiconductor material, anintrinsic semiconductor material, and a n-type semiconductor material,respectively. In another embodiment, the semiconductor core 206, theabsorber sublayer 205, and the absorber sublayer 204 may be a n-typesemiconductor material, an intrinsic semiconductor material, and ap-type semiconductor material, respectively.

In an embodiment, the semiconductor material for the core 206 and theabsorber sublayers 204, 205 may be different materials. For example, thecore 206, the absorber sublayers 205, 204 may include p-type cadmiumtelluride, intrinsic cadmium telluride, and n-type cadmium sulfide,respectively. In an alternative example, the core 206 and the absorbersublayers 205, 204 may include a n-type cadmium sulfide, intrinsiccadmium telluride, and a p-type cadmium telluride, respectively.

In an embodiment, the semiconductor materials for the semiconductor core206 and the absorber sublayers 204, 205 may be the same semiconductormaterials. For example, the semiconductor core 206, the absorbersublayers 205, 204 may include a p-type amorphous silicon, an intrinsicamorphous silicon, and a n-type amorphous silicon, respectively. In analternative example, the semiconductor core 206 and the absorbersublayers 205, 204 may include a n-type amorphous silicon, an intrinsicamorphous silicon, and a p-type amorphous silicon.

The semiconductor core 206 may be made from one or more of silicon,amorphous silicon, polycrystalline silicon, single crystal silicon,cadmium telluride, gallium arsenide, cadmium sulfide, copper indiumselenide, and copper indium gallium selenide. The absorber sublayers orregions 204, 205 may be made from one or more of silicon, amorphoussilicon, polycrystalline silicon, single crystal silicon, cadmiumtelluride, gallium arsenide, cadmium sulfide, copper indium selenide,and copper indium gallium selenide.

FIG. 8 illustrates an embodiment method 800 for manufacturing aphotovoltaic cell made up of an array of photovoltaic bristles asdescribed above. In block 802 a substrate may be formed. In anembodiment, the substrate may be formed by selecting a base material andforming the substrate material to a desired shape. As discussed abovethe substrate may be glass, doped semiconductor, diamond, metal, apolymer, ceramics, or a variety of composite materials.

In block 804 approximately cylindrical cores may be formed on thesubstrate. In an embodiment, cylindrical cores may be formed by avariety of processes. For example, metal cores may be grown up from thesubstrate through a mask using plating, vapor deposition and othersimilar well known processes. As another example, semiconductor coresmay be grown up from the substrate using vapor deposition methods wellknown in the semiconductor processing parts. Plastic polymer cores maybe made by molding or stamping cylindrical cores out of the substrate.In another embodiment, cylindrical cores may be formed by depositing acore layer over the substrate and stamping cylindrical cores out of thedeposited core layer. In another embodiment, cylindrical cores may beformed by depositing a core layer over the substrate and etchingcylindrical cores from the deposited core layer. In another embodiment,cylindrical cores may be formed by placing a template over the substrateand depositing material into the template, thereby forming cylindricalcores. The cores formed in the processes of block 804 may position andsize the cores with dimensions and spacing determined using the designequations described above.

In optional block 806 the cylindrical cores may be further processed,such as to increase the structural strength of the cylindrical coresformed in block 804. The operations of optional block 806 may beperformed in embodiments in which the cylindrical cores are made of anon-conductive materials, such as a polymer. As an example, thecylindrical cores may be processes to form a rigid shape (e.g., acylinder) by exposing them to elevated temperatures or electromagneticradiation that leads to a hardening process. Processes that may beaccomplished in optional block 806 may include processes that promotepolymerization, cross-linking, or curing to make the material strongeror more rigid.

When the core material is nonconductive, in optional block 808 an innerconductive layer may be formed on the cylindrical cores. In thisprocess, the conductive layer may be applied with the thicknesssufficient to conduct the expected amount of current when thephotovoltaic cells are exposed to the design level of insolation. In anembodiment, the inner conductive layer may be formed by striking aconductive layer onto the cylindrical cores. In another embodiment, aninner conductive layer may be formed by depositing the inner conductivelayer by any of chemical vapor deposition, plasma-enhanced chemicalvapor deposition, atomic layer chemical vapor deposition, sputtering,plating, physical vapor deposition, ion plating, and coding with awet-chemical process.

In block 810 an absorption layer may be formed over the cylindricalcores. In an embodiment, the absorption layer may be formed bysequentially depositing a number of semiconductor sublayers over thecore. For example, a p-type cadmium telluride sublayer may be appliedfollowed by application an n-type cadmium sulfide sublayer. In anembodiment, the absorption layer may be deposited using well-knownsemiconductor processing techniques, such as by chemical vapordeposition, plasma-enhanced chemical vapor deposition, atomic layerchemical vapor deposition, physical vapor deposition, ion plating,sputtering, etc. As part of block 810, each of the applied semiconductorsublayers may be further processed, such as to apply a desired level ofdopant to generate the p-type or n-type semiconductor material in theregion of the junction, and/or to adjust the index of refraction of thelayer.

In block 812 an outer conductive layer may be formed over the absorptionlayer. In an embodiment, the outer conductive layer may be depositedusing well-known semiconductor and solar cell manufacturing methods,such as by chemical vapor deposition, plasma-enhanced chemical vapordeposition, atomic layer chemical vapor deposition, physical vapordeposition, ion plating, sputtering, etc. As part of block 812, outerconductive layer may be further processed, such as to adjust the indexof refraction of the layer.

In an alternative method, the photovoltaic bristles may be created inthe reverse direction with a non-solid core. Nanoprinting techniqueswell known in the art may create an array of vias out of an opticallytransparent material (e.g., a transparent conductive oxide, atransparent conductive nitride, or an optically transparent polymer).Alternatively, vias could be formed by etching or ablation of a glassmaterial. The absorption layer including any number of sublayers may beformed within the vias and as well as over the optically transparentmaterial between the vias. The deposition methods used to deposit thesemiconductor layers into vias may be similar to those used indepositing semiconductor layers over the core (e.g., chemical vapordeposition). An inner conductive layer (i.e., a back conductor layer)may be formed within and between the vias over the last semiconductorlayer. The inner conductive layer may be added by sputtering orevaporative techniques well known in the art. When the device iscompleted, the vias are rotated 180 degrees presenting the opticallytransparent layers outward. Thus, depending on the material thicknessused for the back conductor layer, a void may remain in the viasresulting in a non-solid core.

As mentioned above, in addition to increasing the percentage of photonsabsorbed and converted into electrical energy, the various embodimentphotovoltaic bristle structures also exhibit unexpected improvements inelectrical conductivity when exposed to light energy. This effect hasbeen observed in prototypes, and may be due, at least in part, toelectric field effects in the transparent conductive layer caused byelectric field concentrations at the points of discontinuities (e.g.,sharp corners) in the structures. The photovoltaic bristle structure ofthe various embodiments features discontinuities in the outer conductivelayer. These structural discontinuities occur at the base, (i.e., wherethe bristle couples to the substrate) and near the tip of each bristle.When the photovoltaic bristles are exposed to light the photovoltaiceffect in the photovoltaic layer causes electrons and holes to move tothe inner and outer conductive layers. Due to the surface shapes at thebase and tip of the photovoltaic bristles, which form sharp corners, theelectric charge on the surface may be greater in these locations thanthat exhibited in traditional planar photovoltaic cells. More important,the discontinuities near the connection of the bristle to the substrateand near the tip may result in substantially higher electric fields inthe transparent conductive layer in these regions. Testing of prototypesof embodiment photocells have detected surprisingly low resistance ofthe transparent conducting layer when the cell is exposed to light. Thissubstantial reduction in electrical resistance in the transparentconductive layer may reduce the electrical losses due to resistancethrough the photovoltaic cell. Consequently, more electricity may beproduced from an embodiment photovoltaic cell than would be expectedconsidering the normal resistance of outer conductive layer materials.

While the specific physics involved in reducing the electricalresistance of the outer conductive layer (e.g., a transparent conductiveoxide) are not fully understood, testing of the prototypes suggests thatthe effect may be related to the electric field concentrations in thestructural discontinuities at the tip and base of the photovoltaicbristles. One possible explanation, although not intended to be alimitation on the claims, is that the electric field concentrations inthese regions of the photovoltaic bristles result in a change in theelectrical resistance of the materials similar to what occurs in a fieldeffect transistor when an electric field is applied. By significantlydecreasing the electrical resistance in the regions of high electricfield concentrations, the average electrical resistance through theouter conductive layer across an array of photovoltaic bristles may besubstantially reduced. This effect is believed to be related to shapesand sizes of embodiment photovoltaic bristle structures, and thus uniqueto the structures of the various embodiments.

The electric field concentration effects are illustrated in FIG. 9. FIG.9 illustrates an embodiment in which the semiconductor materials in theabsorption sublayers 504, 506 are arranged such that electrons migrateto the outer conductive layer 203 and holes migrate to the conductivecore 206. This is strictly for illustration purposes, because in otherembodiments the polarity of the absorption sublayers 504, 506 may bereversed such that electrons migrate to the conductive core 206. Asillustrated in FIG. 9, electrons and holes along the length of thephotovoltaic bristles (i.e. in the regions 904 and 908) will flowthrough the inner and outer conductive layers 206, 203, resulting in anaverage field concentration that is a function of the rate of photonabsorption. Current flowing from these regions 904 and 908 to theconductors on the substrate 102 will encounter structuraldiscontinuities where the bristle joins the substrate, which can lead toa concentration of charges 902, 906. Similar field concentrations mayoccur near the corners the tips of the photovoltaic bristles asillustrated. This concentration of charges at the tips and base of thephotovoltaic bristles may result in an increased electric field betweenthe concentrations electrons 902 on one conductive layer and of holes906 on the opposite conductive layer. This local concentration electronsand holes may result in a locally enhanced electric field, which isbelieved to be at least part of cause the observed reduced electricalresistance in the outer conductive layer.

FIG. 10A-10D illustrates the multiple embodiments for the outerconductive layer 203. FIG. 10A illustrates that the outer conductivelayer 203 may comprise multiple layers as shown in the examples in FIGS.10B-10C. Although FIGS. 10B-10C only illustrate up to three sublayerswithin the outer conductive layer 203, any number of sublayers andcombinations of materials for these sublayers are envisioned. Forexample, an outer conductive layer may include five sublayers with threethin conductive sublayers separated by two non-conductive sublayers. Byincluding multiple sublayers, the outer conductive layer 203 may includea total thickness that achieves the proper optical depth (d_(ocl)) forenhanced transmissive properties in the design equations while alsoincluding a thin conductive sublayer providing the added field effectbenefits described above. Additionally, the multiple sublayers withinthe outer conductive layer 203 may add flexibility to each photovoltaicbristle 201.

To help achieve an outer conductive layer 203 thick enough to exhibithigh transmissive properties while simultaneously thin enough to exhibitthe field effect benefits within each photovoltaic bristle 201, theouter conductive layer 203 may include two sublayers including aconductive sublayer 1012 (T_(C)) and a non-conductive sublayer 1014(T_(NC)) as shown in FIG. 10B. The conductive sublayer may be anysuitable transparent conductive material with a thickness ofapproximately 500 to 15,000 angstroms. Some suitable transparentconductive materials may include, a transparent conductive oxide (e.g.,indium tin oxide, zinc oxide, titanium oxide, etc), a transparentconductive nitride (e.g., titanium nitride), or a transparent conductivepolymer. Alternatively, the conductive sublayer 1012, may include a thinmetal conductor such as gold or nickel to achieve a high conductivefield effect. The non-conductive sublayer 1014 may be any opticallytransparent material known in the art such as a non-conductive opticallytransparent polymer, an optically transparent gel, or a dielectriclayer, which makes up the difference between the thin conductivesublayer 1012 and the required thickness (d_(ocl)) for the entire outerconductive layer 203. The non-conductive sublayer 1014 and theconductive sublayer 1012 may match the required index of refraction(n_(ocl)) for the outer conductive layer 203. Instead of including anon-conductive sublayer 1014, the outer conductive layer 203 may includetwo different conductive sublayers 1012, 1016 as shown in FIG. 10C. Forexample, the outer conductive layer 203 may include a transparentconductive oxide such as titanium oxide (TiO₂) and a transparentconductive nitride such titanium nitride (TiN). The two conductivesublayers 1012, 1016 may combine to achieve the required optical depth(d_(ocl)) for the design formulas while individually being thin enoughto exhibit the field effect benefits. In an embodiment, the outerconductive layer 203 may include three sublayers such as anon-conductive sublayer 1014 separating two conductive sublayers 1012,1016 as shown in FIG. 10D. The two conductive sublayers 1012, 1016 mayeach exhibit field effects leading the outer conductive layer 203 andthe photovoltaic bristle 201 to have benefits from the multiple fieldeffects. Additionally, the non-conductive sublayer 1014 combined withthe two conductive sublayers 1012, 1016 may provide better transmissiveproperties by achieving a desired total thickness in the outerconductive layer 203 as well as adding flexibility to the photovoltaicbristle 201 than only having a single thin conductive layer exhibitingfield effects.

As described above, reductions in resistance of the transparentconductive layer due to electric field effects transparent conductionallows for the use of very thin transparent conductive layers inembodiment photovoltaic bristles. Prototype embodiment photovoltaiccells have been manufactured with transparent conductive layers with athickness of 1500 angstroms. Based on analysis and such testing, it isbelieved that thinner transparent conductive layers may be achievable.Thinning the transparent conductive layers may enable the use of smallerdiameter cores and/or the addition of a transparent optical layer overthe transparent conductive layer.

As mentioned above, the wave interactions of photons with arrays ofphotovoltaic bristles designed according to the embodiment designequations described above have been analyzed using classicalelectrodynamics and quantum mechanical models. These electrodynamic andquantum mechanical models take into account the wave interactions ofphotons with the regular and close spaced array of photovoltaicbristles, as well as the wave interactions with the transparentconducting oxide layer, and other layers in the design. Theseelectrodynamic and quantum mechanical models also account for theinternal refraction characteristics described above that are enabled byproperly selecting the layer materials and thicknesses. These analysesreveal that a large fraction of the photons entering an embodiment arrayof photovoltaic bristles are absorbed into the bristles, where a largefraction of the incident photons are absorbed in the photovoltaicmaterials. These analysis results are illustrated in FIG. 11 whichillustrate the probability of finding a photon at a given location interms of brightness (i.e., dark regions are where there is a lowprobability that a photon exists). Specifically, FIG. 11 illustratesthat photons striking an array of photovoltaic bristles are quicklyabsorbed into and largely remain trapped within the transparentconducting oxide and photovoltaic absorption layers.

The preceding description of the disclosed embodiments is provided toenable any person skilled in the art to make or use the presentinvention. Various modifications to these embodiments will be readilyapparent to those skilled in the art, and the generic principles definedherein may be applied to other embodiments without departing from thespirit or scope of the invention. Thus, the present invention is notintended to be limited to the embodiments shown herein but is to beaccorded the widest scope consistent with the following claims and theprinciples and novel features disclosed herein.

What is claimed is:
 1. A photovoltaic cell, comprising: an array ofphotovoltaic bristles located over a substrate, wherein eachphotovoltaic bristle comprises: a core having a core radius (r_(c)) inthe range of about 0.5 microns to 50 microns: a portion of a contiguousabsorption layer comprising photovoltaic semiconductor materialpositioned over the core and having a first radial thickness (d_(abs))in the range of 0.2 microns to 1.0 microns; and a portion of acontiguous outer conductive layer positioned over the absorption layer,having a second radial thickness (d_(ocl)) in the range of 0.2 micronsto 1.0 microns and an index of refraction (n_(ocl)), wherein acombination of the substrate and the cores of the photovoltaic bristlesis made of a base material portion and a metal layer that covers thebase material portion, each core including a protruding portion of themetal layer, wherein the contiguous absorption layer is located overeach of the cores of the photovoltaic bristles, wherein a bottommostlayer within the contiguous absorption layer includes a planar portionlocated between the cores and overlies a portion of the metal layer thatextends between the cores, wherein the contiguous outer conductive layercontacts sidewall surfaces and a planar top surface of the contiguousabsorption layer between the cores, wherein each bristle is configuredsuch that:$\frac{n_{ocl}*r_{c}}{n_{amb}*\left( {r_{c} + d_{abs} + d_{ocl}} \right)} \leq 1$wherein n_(amb) is the index of refraction of an ambient materialsurrounding the bristles, wherein each photovoltaic bristle in the arrayof photovoltaic bristles extends from a major surface of the substrateand has a longitudinal axis oriented transverse to the major surface ofthe substrate; and wherein the height of each photovoltaic bristle alongthe bristles longitudinal axis is in the range of 0.1 microns to 100microns.
 2. The photovoltaic cell of claim 1, wherein the second radialthickness (d_(ocl)) is smaller than the first radial thickness(d_(abs)).
 3. The photovoltaic cell of claim 1, wherein an absorptionlayer index of refraction (n_(abs)) is greater than the outer conductivelayer index of refraction (n_(ocl)).
 4. The photovoltaic bristle ofclaim 1, wherein the absorption layer is made from semiconductormaterial selected from the group of silicon, amorphous silicon,polycrystalline silicon, single crystal silicon, cadmium telluride,gallium arsenide, aluminum gallium arsenide, cadmium sulfide, copperindium selenide, and copper indium gallium selenide.
 5. The photovoltaicbristle of claim 1, wherein the outer conductive layer is made from oneor more of zinc oxide, indium tin oxide, cadmium tin oxide, titaniumoxide, and a transparent conductive nitride.
 6. The photovoltaic bristleof claim 5, wherein the outer conductive layer comprises a conductivesublayer and a non-conductive sublayer.
 7. The photovoltaic bristle ofclaim 1, wherein the core comprises: an inner core made from anon-conductive material; and the metal layer surrounding the inner core,wherein the metal layer comprises one or more of gold, copper, nickel,molybdenum, iron, aluminum, and silver.
 8. The photovoltaic bristle ofclaim 1, wherein a height (h_(min)) of the photovoltaic bristlessatisfies the equation:$h_{\min} = {\frac{\left( {\left( {\left( {1.67*d_{abs}} \right) + r_{c}} \right)*(2)*(0.9)} \right)}{\tan\left( {40{^\circ}} \right)}.}$9. The photovoltaic bristle of claim 1, wherein the array ofphotovoltaic bristles are arranged such that an edge to edge spacingbetween neighboring photovoltaic bristles (P_(EtoE)) satisfies theequation:((1.67*d _(abs))+r _(c))*(2)*(0.9)≦P _(EtoE)<((1.67*d_(abs))+r)*(2)*(1.1).
 10. The photovoltaic cell of claim 1, wherein thearray of photovoltaic bristles are configured to form a photon absorbingmetamaterial.
 11. The photovoltaic cell of claim 1, wherein the ambientmaterial is air and n_(amb) is the index of refraction of air.
 12. Thephotovoltaic cell of claim 1, wherein the ambient material is atransparent solid having an index of refraction greater than that ofair.
 13. The photovoltaic cell of claim 1, wherein the bristles have amedian radius (r_(m)) of between 0.5 microns and 3 microns.
 14. Thephotovoltaic cell of claim 1, wherein the bristles have a mean radius(r_(m)) of between 0.5 microns and 1 microns.
 15. The photovoltaic cellof claim 13, wherein the bristles have a height of between 0.5 micronsand 20 microns.
 16. The photovoltaic cell of claim 13, wherein thebristles have a height of between 5 microns and 15 microns.
 17. Thephotovoltaic cell of claim 16, wherein the bristles have a height ofbetween 8 microns and 10 microns.